Three fair, standard six-sided dice are rolled. What is the probability that the sum of the numbers on the top faces is 18? Express your answer as a common fraction.
Solution: We quickly note that the only way for three dice to sum to 18 is for the face of each to be a 6. So, if each die is a 6, then the probability of this occurring is $\frac{1}{6^3} = \boxed{\frac{1}{216}}$.